# If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent,in how many points will they intersect each other

$\begin{array}{1 1}(A)\;180\\(B)\;190\\(C)\;200\\(D)\;210\end{array}$

Toolbox:
• $n!=n(n-1)(n-2)(n-3)...(3)(2)(1)$
Let us draw line 1 by 1
$1^{st}$ line =0 points
$2^{nd}$ line =new 1 point
$3^{rd}$ line =new 2 points+old 1 point
$4^{th}$ line =new 3 points +old 2+1 points
$n^{th}$ line =(n-1)points +(n-2).....(3)(2)(1)
$\therefore S=1+2+3.....(n-1)$
$S=(n-1)\times \large\frac{n}{2}$
$\Rightarrow 19\times \large\frac{20}{2}$
$\Rightarrow 19\times 10$
$\Rightarrow 190$
Hence (B) is the correct answer.